Eureqa!

I've been feeding my relentless hunger for RadioLab episodes, and have thus far suffered no negative consequences for having done so (other than a slightly hyperextended mind, but that's a price I'm willing to pay). One of my most recent listens was an episode entitled "Limits," in which Jad, Robert and crew explore the limits of the human body, mind, and knowledge. Overall it was an absolutely fascinating episode, probing the mind-boggling extremes of which humans are capable, and the respective consequences of those extremes. Most fascinating to me was the third act exploring the limits of "human knowledge." Do yourself a favor and listen to it here (it's only 11 minutes long):



An interesting distinction is made near the beginning of the act, which seems to me to be the fundamental insight in the entire piece: the distinction between knowledge and understanding. Dr. Steve Strogatz illustrates the distinction using the example of large numbers. We can simultaneously know and understand small numbers like one, two, ten or even one hundred. But once we move beyond one hundred, those numbers become rather abstract, to the point that numbers like "one trillion" are--while perhaps knowable as the number 1,000,000,000,000--are rather incomprehensible at a personal, existential level (can you actually imagine one trillion of anything?). As data and scientific discoveries become more complex, knowledge continues to increase. But what begins to decrease at these levels of complexity is our appropriation of this knowledge: we cease being able to have those "Eureka!" or "Oooooh, I get it!" moments that, as Jad says, you can 'feel in your bones.' So perhaps this act, using Dr. Strogatz's distinction, is more aptly titled the "Limits of Human Understanding."

The most striking example of this was the story of the computer program Eureqa, developed at Cornell University. As the story tells us, Eureqa is able to take vast amounts of observable data and--after producing numerous hypothetical equations--can actually discover the mathematical laws governing the event that it "observes." After re-discovering Newton's second law of motion by observing a double pendulum, Eureqa went on to discover elegant mathematical representations of bafflingly complex natural systems. So with the collection of enough data and the application of increasingly complex algorithms, it seems that human knowledge, with the help of technology, is--potentially--limitless.

But when Dr. Gurol Suel used Eureqa to find the mathematical law governing a simple bacterium, it wasn't so much a surprise that Eureqa had "found it," and quickly. It was, rather, that the beautifully simple equation that the program had discovered was incomprehensible. That is, while the equation worked, and could even predict the future chemical states of the cell, Dr. Suel and company could not understand why. Ironically, the Eureqa program fails to deliver that Archimedean result to which its name refers: the flash of insight--the "Aha" moment--in which the underlying reasons for "why" the equation works coalesce in a profound grasp of the concept.

And this may very well be the face of science in the future. Dr. Strogatz:

But that will leave us, if this really happens, in some weird position as bystanders where we're sort of listening to the Oracle but not really understanding the answer... We've had this window in human history when we could not just know things but understand them. That is you could know why they were true, not just know, but to know why. And that's a beautiful moment in human history, but I feel like it may only be a moment.

While it's entirely possible that, given enough time and resources, Dr. Suel could reach an understanding of why Eureqa's formula works to describe his bacterium, I think Dr. Strogatz makes a plausible claim: there's also a possibility that understanding more complex phenomena is entirely beyond our capacity to do so.

It's just interesting to think that, if this ever becomes the case, just how similar the natural sciences would become to something like theology: there would be certain doctrines that would be accepted as True (from intelligent machines like Eureqa), and the scientist would then struggle to come to a deeper understanding of these laws using the evidence available to him or her, all the while knowing that a "perfect" understanding could be all but impossible. The analogy is not a perfect one, but its food for thought, I think.